Gerhard Schellhorn and Wolfgang Ahrendt the Wam Case Study: Verifying Compiler Correctness for Prolog with Kiv
نویسنده
چکیده
This chapter describes the first half of the formal, machine-supported verification of a Prolog compiler with the KIV system. Our work is based on the mathematical analysis given in (Börger and Rosenzweig, 1995), where an operational semantics (an “interpreter”) for Prolog is defined as an Abstract State Machine (ASM). This interpreter is then transformed in 12 systematic refinements to an ASM which executes machine code of the Warren Abstract Machine (WAM). The goal of our case study was to formalize ASMs and the proof techniques given in (Börger and Rosenzweig, 1995), and to give machine-checked correctness proofs for the correctness of the refinements. So far we have verified the first 6 refinements, and we will give a detailed account on the problems we found in verification. Our motivations for beginning such a large case study — based on our current experience we estimate the necessary effort to develop a verified compiler to be around a person year — are the following Mathematical analysis is an indispensable prerequisite for formal verification to be applicable. Nevertheless mathematical analysis will always omit details and have minor errors. These errors are due to the large complexity of correctness proofs, which is easily underestimated at first glance. The errors usually do not invalidate the analysis, but would still result in erroneous compilers. We want to demonstrate that the absence of errors can be guaranteed by formal correctness proofs, making them a suitable counterpart to mathematical analysis. We want to show that Dynamic Logic (DL) as it is used in the KIV system can serve as a suitable starting point for the verification of Abstract State Machine refinements. In particular, the proof technique of commuting diagrams of Proof Maps, used informally in (Börger and Rosenzweig, 1995), can be formalized in DL.
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